Mapping spherical seismic into physical structure: biases from 3-D phase-transition and thermal boundary-layer heterogeneity

P>Earth's mantle is, to a very good first approximation, spherically symmetric, with lateral deviations in seismic velocities and density of only a few per cent. This observation has led to the common assumption that average radial seismic models reflect the mantle's average physical structure. We test this assumption by using a set of dynamically generated mantle structures and comparing seismic velocities for the average radial physical state with laterally averaged seismic velocities. The thermal and thermochemical dynamic circulation models are Earth-like in terms of convective vigour, thermal structure and geographical pattern of heterogeneity. We find that, in general, averaged seismic structure is not distinguishable from the seismic structure of the physical average, within the uncertainty bounds of seismic reference models. An exception is near phase boundaries, where phase-boundary topography broadens the averaged seismic jump relative to the discontinuity at physical reference conditions. In an inversion for 1-D seismic structure, where narrow discontinuities are imposed, these biases may map into a lower jump, and substantially stronger velocity gradients above and below the interface than are actually present. Other small biases in averaged structure occur in thermal boundary layers, including those that form above chemical piles. These biases are caused by large lateral variations in temperature, not compositional variability.